Question

Find the value of : cos^-1 ( cos 2 /3 ) + sin^-1 ( sin 2 /3 ) .

Answer 1

$$\begin{gathered} Asweknowthat{\cos }^{-1}\left(\cos x\right)=xifx\in \left[0,\mathrm{\pi }\right] \\ {\sin }^{-1}\left(\sin x\right)=xifx\in \left[\frac{-\mathrm{\pi }}{2},\frac{\mathrm{\pi }}{2}\right] \\ andhereinthequestionthevaluesofxarelyingintheabovementionedregionso, \\ {\cos }^{-1}\left(\cos \frac{2}{3}\right)+{\sin }^{-1}\left(\sin \frac{2}{3}\right) \\ =\frac{2}{3}+\frac{2}{3} \\ =\frac{4}{3} \end{gathered}$$